Commerce Fresh Retail: A Counterfactual Prediction and Multi-Period Op-
timization Approach. In The 27th ACM SIGKDD Conference on KnowledgeDiscovery and Data Mining (KDD ’21), August 14–18, 2021, Virtual. ACM,
New York, NY, USA, 10 pages. https://doi.org/10.1145/nnnnnnn.nnnnnnn
1 INTRODUCTIONIn a fresh retail scenario, the freshness of goods is the main concern
of the customers. Many perishable products, such as vegetables,
meat, milk, eggs, bread, have a limited shelf life. To provide fresh
and high-quality goods, it is very important to control inventory.
If goods have not been sold out before their expiry date, the re-
tailer will have a substantial loss. To maximize the total profit,
promotional markdown is a common approach for e-commerce
fresh retails. However, typically, the retailer does not know what is
the best discount price and often chooses an empirical discount on
goods (such as 30% off, 50% off), which is usually not the optimal
solution.
In this paper, we consider the e-commerce retailer that its fresh
store has two channels for selling goods: the normal channel, wheregoods are sold by no-discount retail price, and the markdown chan-nel, where customers can buy goods by discount under the condition
that their total purchase has reached a certain amount. In particular,
we consider the well-known e-commerce fresh retail - Freshippo1.
As shown in Figure 1, customers can either buy goods in normal
channel with the retail price or buy them in markdown channel
with the discount price. In order to maximize the profit, the retailer
needs to answer two questions. First, can goods be sold out with
the retail price before its expiry date? Second, if not, what is the
optimal discount price for promotional markdown to ensure the
goods being sold out while maximizing the profit? The first problem
is about sales forecasting [9, 23], and the second problem is about
price-demand curve fitting and price optimization [8, 10, 11, 28].
This paper focuses on the second problem. Specifically, we consider
the multi-period dynamic pricing problem of a perishable product
sold in markdown channel over its shelf life. Our aim is to learn
price-demand model rightly and optimize price over a multi-period
time horizon dynamically.
1Freshippo (https://www.freshhema.com/) is an online-to-offline (O2O) service plat-
form provided by Alibaba group. It takes the online shopping experience to bricks-
and-mortar stores. It integrates the online and offline stores, uses artificial intelligence
technology and operations research methods to provide customers best shopping
Figure 1: An example of normal channel and markdownchannel on Freshippo.
The main challenge of demand learning is that the price of most
of goods are changed infrequently for fairness, and some even
never be changed. It is hard to predict the sales of a product at the
discount price which is not observed before. In the literature of
causality, this problem is called counterfactual inference [25–27],
where the price is the treatment/intervention of the markdown
and the sales is the outcome of the markdown. We are interested
in studying how the outcome changes with different values of
the intervention. For example, suppose we observe the sales of a
product with price A and B, we aim to predict the sales of a product
with price C, which is counterfactual. The seller can use the price
experimentation for demand learning, however the randomized
control trail is too costly and has a risk of price discrimination.
Alternatively, we focus on the observational study for learning
price-demand curve. In other words, we attempt to learn price-
demand function from the observational data. It is infeasible to
learn individual demand function of a product using only its own
data due to the limited price change. Nevertheless, it is possible to
jointly learn the price-elasticity of plenty of products with shared
parameters. Therefore, we collect abundant feature and historical
transaction data of all kinds of products, possibly in different stores.
To learn the demand function, a naive approach is using machine
learning-based predictive model. It treats price as one of input
features and treats sales as label, and fits the model by minimizing
factual error. However, the small factual error does not mean a
small counterfactual error since the counterfactual distribution
may be very different with factual distribution [22, 32]. Besides,
when features are correlated with the price (such as historical sales),
the importance of price will be largely dominated. Moreover, since
Target,Inventory and PriceConstraints
HistoricalObservational
Data
Base SalesForecasting
Price ElasticityLearning
Semi-ParametricStructural Model
CounterfactualPrediction
MDP Optimization OnlineMarkdown
Data Layer Algorithm Layer Application Layer
Figure 2: Our framework for markdowns in fresh retail.
most of the machine learning models are complex or even black-
box, it is difficult to reveal the true relationship between price and
demand. Therefore, most of ML models have weak interpretability.
To tackle with this problem meanwhile making use of rich fea-
tures, we propose a novel data-driven semi-parametric structuralmodel to capture the price-demand curves. This semi-parametric
model establishes a connection between black-box machine learn-
ing model and economic model, where the role of ML model is to
predict the baseline demand, and the role of economic model is
to build a parametric and explainable price-demand relationship,
namely price elasticity. To learn price elasticity of individual prod-
uct, we make use of the shared information among products and
propose a multi-task learning algorithm. Based on this framework,
the learned elasticity is stable and the counterfactual prediction is
reliable.
Using the counterfactual prediction results, the aim of price
optimization is to choose the best discount under some business
constraints to maximize the overall profit. Note that a fresh retail
usually has many stores in a region. For example, Freshippo has
more than 50 stores in Shanghai. To avoid price discrimination, the
discounts of the same product in different stores within the same
region should be all equal. Therefore, to optimize the discount price,
we need to take all stores in a region into consideration. Besides,
since both demand and inventory of a product would be changed
with different stages of product life time horizon, the retailer would
like to take dynamic pricing strategy for markdowns. Moreover,
note that the forecasting results obtained by counterfactual pre-
diction will inevitably have randomness as the variance and bias
occurred in the learning procedure. To improve the robustness of
the algorithm, it is better to model the demand uncertainty. For
these reasons, we split the life cycle of a product into multiple pe-
riods and optimize the discount price of each period to maximize
the overall profit. We present a multi-period joint price optimiza-tion formulation using Markov decision process. Since the number
of the state grows exponentially with the number of stores, tra-
ditional dynamic programming method suffers from the curse of
dimensionality. To solve this problem, we develop an efficient two-
stage algorithm. It reduces the time complexity from exponential
to polynomial. To demonstrate the effectiveness of our approach,
we present both offline experiment and online A/B testing at Fre-
shippo. It is shown that our approach has remarkable improvements
compared to the manual pricing strategy.
The main contributions are summarized as follows:
• We propose a new learning-and-pricing framework based on
counterfactual prediction and multi-period optimization for
markdowns of perishable goods, especially for e-commerce
fresh retails, as shown in Figure 2.
• We propose a semi-parametric structural model that taking
advantage of both predictability and interpretability for pre-
dicting counterfactual demand, and present a multi-perioddynamic pricing approach which takes the demand uncer-
tainty into consideration, and finally design a very efficient
two stage pricing algorithm to solve it.
• We successfully apply the proposed pricing algorithm into
the real-world e-commerce fresh retail. The results show
great advantage.
2 RELATEDWORKThis paper addresses the important data science problem, mark-
down optimization, which focuses on the dynamic pricing problem
where the price of a perishable product is adjusted over its finite
selling horizon. It is a variant of revenue management (RM), and
has been studied in areas of marketing, economics, and operations
research [29]. Most of studies address the static price optimization
problem using descriptive models [4, 5, 33]. We focus on multi-
period dynamic pricing optimization with demand uncertainty us-
ing the prescriptive model.
In the literature, some researchers have developed pricing deci-
sion support tools for retailers. For example, a multiproduct pricing
tool is implemented for fast-fashion retailer Zara for its markdown
decisions during clearance sales [6]. For recommending promotion,
the researchers present randomized pricing strategies by incorpo-
rating some new features into electronic commerce [34]. In [10],
the researchers develop a multiproduct pricing algorithm that in-
corporates reference price effects for Rue La La to offer extremely
limited-time discounts on designer apparel and accessories.
In the context of machine learning, some regression methods
have been applied for demand learning. Most of existing works are
based on linear regression with different linear demand models for
its ease of use and interpretation, such as strict linear, multiplicative,
exponential and double-log model [17]. Other works consider the
market share of products and use choice model to model demands
of products, such as multinomial logit model, nested logit model
[21]. Some researchers use semi- and non-parametric models for
demand learning. In [24], the authors use SVM to evaluate retailer’s
decisions about temporary price discounts. In [16], the authors use
multilayer perceptrons to estimate store-specific sales response
functions. However, these methods can not work well when the
price of a product is seldom changed in the historical data, which
is common in real-world scenario.
Some recent approaches usemachine learningmethods for causal
inference, such as trees [1, 2] and deep neural networks [22, 32].
But these methods are designed for binary treatment. In [13], the
authors presents a deep model for characterize the relationship be-
tween continuous treatment and outcome variables in the presence
of instrument variables (IV). However, the IV itself is hard to be
identified, which limits the scope of its application.
85
32 2825
8 10 7
3 4
1-class category
2-class category
3-class category
sku 1 sku 2 sku 3
... ...
root
... ...
Figure 3: An example of the data aggregation structure bycategories. The number in a circle represents the number ofthe observed data aggregated in that category.
In the literature of price optimization, some researchers consider
the large scale pricing problem of multiple products and propose
algorithms based on network flow [18], semi-definite programming
relaxation [19] and robust quadratic programming [35]. In [36], the
authors consider pricing problem in multi-period setting, and use
robust optimization to find adaptable pricing policy. However, this
model is designed for monopoly and oligopoly and is not suitable
for e-commerce fresh retail scenario.
3 PROBLEM FORMULATIONLet us consider an e-commerce retail who wants to sell out 𝑁 prod-
ucts by markdowns. These products are possibly sold in different
stores in a region. Our task is to offer the optimal discount price
for these products to maximize the overall profit of all stores.
Instead of using the absolute value of price, we use the relative
value, i.e. the percentage of retail price 𝑑 ∈ [0, 1], as the decisionvariable (treatment/intervention) of markdowns, as the range of
the percentage discount is fixed and finite while the price itself
is infinite. Thus, we can jointly learn price elasticity of different
products who have different price magnitudes. Let us denote 𝑌𝑜𝑏𝑠𝑖
as the average sales of product 𝑖 at the discount 𝑑𝑖 in markdown
channel in the past days. We collect a set of observable covariate
features 𝒙𝑖 ∈ R𝑛 , including categories, holidays, event information,
inherent properties and historical sales of products and shops, etc.
In particular, we denote categorical feature as 𝐿𝑖 ∈ {0, 1}𝑚 , and
assume there are three level categories.
The proposed pricing algorithm consists of two steps: counter-
factual prediction and price optimization. In next two sections, we
present these two steps respectively.
4 COUNTERFACTUAL PREDICTIONThe key of pricing decision making is to accurately predict the
demand of products at different discount prices. The difficult is that
these prices may never be observed before. In other words, they
are counterfactual [15, 30]. The aim of counterfactual prediction is
to predict the expectation of demand/sales E[𝑌𝑖 |do(𝑑𝑖 ), 𝒙𝑖 ] underthe intervention 𝑑𝑖 and the condition 𝑋 = 𝒙𝑖 , where the do(·) isthe do operator [26].
4.1 Semi-Parametric Structural ModelIn this subsection, we present a semi-parametric structural model
to predict the counterfactual demand. It works under the com-
mon simplifying assumption of “no unmeasured confounding” [14].
Specifically, we make the following assumption:
Assumption 1 (unconfoundedness). The treatment 𝑑𝑖 is con-ditionally independent with potential outcomes 𝑌 (do(𝑑𝑖 )) given theobserved features 𝒙𝑖 , i.e., 𝑑𝑖 ⊥⊥ 𝑌𝑖 (do(𝑑𝑖 )) |𝒙𝑖 .
This ensure the identifiability of the casual effect when the com-
plete data on treatment 𝑑𝑖 , outcome 𝑌𝑖 and covariates 𝒙𝑖 are avail-able. However, in the real-world scenarios, it is almost impossible
to collect the complete data for a single product 𝑖 , especially when
treatment 𝑑𝑖 is continuous. In most cases, the discount on a product
only has one or two different values in the historical transaction
data. Therefore, it is impossible to fit the price-demand curve and
compute individual causal effect using the observational data of a
single product.
To solve this problem, we use the data aggregation technique.
We aggregate data of all products by using the category information
and learn the causal effect of each product jointly. As shown in
Figure 3, a high-level category has many low-level categories, and
a lowest-level category has many different products/SKUs (stock
keeping unit). Note that a higher level category has more SKUs, but
the difference and variance between SKUs also become larger.
Borrowing the ideas from marginal structural model [31], we
propose a semi-parametric structural model to learn individual
casual effect. In detail, we assume the outcome 𝑌𝑖 is structurally
where 𝜽2 ∈ R𝑚 , 𝜽 = [\1, 𝜽𝑇2 ]𝑇, 𝑐 is an intercept parameter and 𝐿𝑖
is a compound of three one-hot variables, namely
𝐿𝑖 = [0, . . . , 1, 0︸ ︷︷ ︸𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦1
, 0, 1, . . . , 0︸ ︷︷ ︸𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦2
, 0, . . . , 1, 0︸ ︷︷ ︸𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦3
]𝑇 . (5)
Since the coefficient of treatment 𝑑𝑖 is modified by 𝐿𝑖 , we call 𝐿𝑖as effect modifiers. By exponential transformation, this model can
also be written as a constant price elasticity model, i.e.,
𝑌𝑖 = 𝑌𝑛𝑜𝑟𝑖 𝑒𝑐𝑑
\1+𝜽𝑇2 𝐿𝑖𝑖
,∀𝑖, (6)
where \1+𝜽𝑇2 𝐿𝑖 is price elasticity of demand, which is structured by
three different level categories. In other words, the price elasticity
of each individual SKU is a summation of a common coefficient
\1 and the elasticity of each category. As we have stated, the ag-
gregated data within high level category has large sample size but
also has large variation, while the aggregated data within low level
category has small variation but also has small sample size. Instead
of learning elasticity within a single category, this model simulta-
neously learns price elasticity of all category-levels which is more
flexible.
To estimate the price elasticity of demand, we can use the mean
squared error criterion with entire samples. However, in the real
world e-commerce retail scenario, the data is generated by stream-
ing. A better alternative is to update the parameters in an online
fashion. Therefore, based on recursive least squares, we update the
parameters by minimizing the following objective function:
min𝜽 ,𝑐
𝑁∑︁𝑖=1
𝑡∑︁𝑗=1
𝜏𝑡−𝑗 | | ln𝑌𝑖, 𝑗
𝑌𝑛𝑜𝑟𝑖, 𝑗
− 𝜽𝑇 𝐿𝑖 ln𝑑𝑖, 𝑗 − 𝑐 | |22 + _ | |𝜽 | |22, (7)
Shop A
Shop B
Shop C
1 2 3 4 5 6Period
Figure 4: An example of the activated shops and index ofmultiple periods. The dotted blue vertical line represents thecurrent time. The dotted grey blocks represent the inactivatedays, and solid blue block represent the activate days.
where 𝐿𝑖 = [1, 𝐿𝑇𝑖 ]𝑇is the augmented variable and _ > 0 is a pre-
defined regularization coefficient, 0 < 𝜏 ≤ 1 is a forgetting factor
which gives exponentially less weight to older samples. The optimal
solution of (7) can be represented by two sufficient statistics, which
are then can be easily updated in an online fashion.
4.4 Counterfactual Demand PredictionSupposewe have obtained the observational data from time 1 to 𝑡−1,our aim become to predict the counterfactual demand of product 𝑖
of time 𝑡 with different discounts. Let us denote the base discount
and base sales of product 𝑖 predicted by the sales forecasting module
as (𝑑𝑜𝑖,𝑡, 𝑌𝑜
𝑖,𝑡), and denote the estimated parameter of price elasticity
model as 𝜽𝑡 . Substituting (3) and (4) into semi-parametric model
where 𝑤 𝑗 > 0 is the weight of waste loss and [·]+ is the non-
negative operator. The variables 𝑙𝑏 𝑗𝑡 and 𝑢𝑏 𝑗𝑡 are respectively
minimum and maximum value of discount for shop 𝑗 at period
𝑡 . Since both 𝑍 𝑗𝑡 and 𝐵 𝑗 are independent with decision variables
{𝑑1, . . . , 𝑑𝑇 }, we can simplify (9) as
max𝑑1,𝑑2,...,𝑑𝑇
∑︁𝑗 ∈J
𝑇𝑗∑︁𝑡=1
(𝑝0𝑑𝑡 +𝑤 𝑗 )𝑌𝑗𝑡 (𝑑𝑡 )
s.t.
𝑇𝑗∑︁𝑡=1
(𝑌𝑗𝑡 (𝑑𝑡 ) + 𝑍 𝑗𝑡 ) ≤ 𝐵 𝑗 , 𝑗 ∈ J
𝑙𝑏 𝑗𝑡 ≤ 𝑑𝑡 ≤ 𝑢𝑏 𝑗𝑡 , 𝑡 = 1, . . . ,𝑇𝑗 , 𝑗 ∈ J ,
(10)
where the first constraint describles the interaction among decision
variables {𝑑1, 𝑑2, · · · , 𝑑𝑇 }.
5.1 MDP ModelThe continuous optimization w.r.t discount is indeed not convex.
However, in this paper, we do not optimize the discount directly.
Considering that the candidates of the discount is finite, we trans-
form it into discrete optimization problem instead. Moreover, note
that the learned price-sales function 𝑌𝑗𝑡 (𝑑𝑡 ) and the predicted nor-
mal sales 𝑍 𝑗𝑡 inevitably have the randomness due to the variance
and bias occurred in the learning and prediction process. In other
words, the parameters in the optimization problem (10) have uncer-
tainty. Therefore, we use Markov decision process (MDP) to model
this decision-making problem.
Without loss of generality, we assume the actual sales of shop
𝑗 in markdown channel and normal channel are respectively 𝑎𝑦
𝑗𝑡
and 𝑎𝑧𝑗𝑡at period 𝑡 . Let us define the state as the inventory in stock,
i.e., the state 𝑠 𝑗,𝑡 represents the inventory of product A at shop 𝑗
at the beginning of period 𝑡 . The initial state of shop 𝑗 is equal to
the target sales or equivalently initial inventory 𝐵 𝑗 . The state 𝑠 𝑗,𝑡+1is equal to the state 𝑠 𝑗,𝑡 subtracting both sales in the markdown
channel and normal channel at period 𝑡 , and the state 𝑠 𝑗,𝑇 will not
be negative at the last period. Mathematically,
𝑠 𝑗,1 = 𝐵 𝑗 ,
𝑠 𝑗,𝑡+1 = 𝑠 𝑗,𝑡 − 𝑎𝑦𝑗𝑡 − 𝑎𝑧𝑗𝑡 , 𝑡 < 𝑇𝑗 ,
𝑠 𝑗,𝑡+1 = 0, 𝑇𝑗 ≤ 𝑡 ≤ 𝑇max .
(11)
Note that the value of state is non-increasing, i.e., 𝑠 𝑗,1 ≥ · · · ≥𝑠 𝑗,𝑇𝑗+1 = 0. We define a set of finite candidates of the percentage
3 3
2
1
0
2
0
11
0
=𝑠𝑗,1 𝐷𝑗 𝑠𝑗,2 𝑠𝑗,3 𝑠𝑗,4
𝑑1
𝑑2
𝑑3
Figure 5: An example of theMarkov decision process of shop𝑗 with 4 states. Circles represent the states and the arrowsrepresent the possible transition directions with action 𝑑𝑡 .For simplicity, we only draw the arrows of blue circles.
discount as D = {𝑑1, 𝑑2, . . . , 𝑑𝑀 }. This discount set is the set ofactions that the decision maker chooses from.
To modeling the uncertainty of sales forecasting algorithm, we
dig into the historical data of the predicted sales and actual sales, and
find that the sales distribution mostly follows Poisson distribution.
In detail, we assume the sales distribution of the markdown channel
follows Poisson distribution with the parameter 𝑌𝑗𝑡 (𝑑𝑡 ), and sales
distribution of the normal channel follows Poisson distribution with
parameter 𝑍 𝑗𝑡 . Since the expectation of the Poisson distribution is
equal to its parameter, we have implicitly assumed that 𝑌𝑗𝑡 (𝑑𝑡 ) and𝑍 𝑗𝑡 are unbiased estimation of 𝑎
𝑦
𝑗𝑡and 𝑎𝑧
𝑗𝑡, respectively.
Let us define 𝑎 𝑗𝑡 := 𝑎𝑦
𝑗𝑡+ 𝑎𝑧
𝑗𝑡as the total sales of product A in
both channels. Since 𝑎 𝑗𝑡 can not be greater than inventory 𝑠 𝑗,𝑡 , we
where the initial value is 𝑄 (𝑠 𝑗,𝑇𝑗+1, ·) = 0, 𝑠 𝑗,𝑇𝑗= 0,∀𝑗 . This is
the bellman equation for each single shop, and it can be updated
by dynamic programming efficiently by finding substructure of
computation.
5.2.2 Joint optimization. We update the𝑄 function using the back-
ward induction separately for each shop until the last step. In the
last step (i.e., at period 1), we can jointly optimize the SKU price
since there is only one state, i.e., 𝑠1 = {𝐵1, 𝐵2, · · · , 𝐵 𝐽 }. The jointoptimization equation can be written as follows,
𝑑∗1 := arg max𝑑𝑡 ∈D
∑︁𝑗 ∈J
𝑄 (𝑠 𝑗,1 = 𝐵 𝑗 , 𝑑1), (17)
where
𝑄 (𝑠 𝑗,1 = 𝐵 𝑗 , 𝑑1) =𝑠 𝑗,1∑︁
𝑠 𝑗,2=0
𝑃 (𝑠 𝑗,2 |𝑠 𝑗,1, 𝑑1)
· (𝑅(𝑠 𝑗,1, 𝑑1, 𝑠 𝑗,2)𝑑 + max𝑑2∈D
𝑄 (𝑠 𝑗,2, 𝑑2)) .(18)
Thus, we obtain the optimal price 𝑝∗1 = 𝑝0𝑑∗1 and the expected
total reward 𝑉 (𝑠1) =∑
𝑗 ∈J 𝑄 (𝐵 𝑗 , 𝑑∗1). Since the pricing algorithm
is performed daily as soon as the new data arrived for each new
day, it will recompute the optimal price for the first period which
is satisfied the price constraint, i.e., the discount price of all shops
are equal. Therefore, it is not necessary that the obtained prices of
different shops are not equal from period 2 to the last period.
For clarity, the pricing algorithm for markdowns in fresh retail
is summarized in Algorithm 1, where we refill the subscript 𝑖 of all
variables to represent product 𝑖 for completeness.
5.3 Time ComplexityIn this subsection, we analyze the time complexity of the proposed
two-stage algorithm. There are at most 𝐵2𝑗∗𝑀 iterations to compute
Q(𝑠𝑡 , 𝑑𝑡 ), where𝑀 is the number of actions. So the time complexity
of two-stage algorithm is𝑂 (𝑇max ∗𝑀 ∗𝐵2max∗ |J |), where 𝐵max :=
argmax𝑗 𝐵 𝑗 . In comparison, note that the state space for a primitive
backward induction method is vector space, and the number of state
is
∏𝑗 ∈J 𝐵 𝑗 . The time complexity for this method is 𝑂 (𝑇max ∗𝑀 ∗
𝐵max
2 |J |), which grows exponentially with the increase of the
Algorithm 1 Pricing algorithm for markdowns of e-commerce
retails
Input: _, 𝜏, 𝜔, 𝒙𝑖, ·, 𝑌𝑜𝑏𝑠𝑖, · , 𝑌𝑛𝑜𝑟
𝑖, · , 𝑑𝑜𝑖, ·,∀𝑖 .
Output: 𝑝∗𝑖,𝑡,∀𝑖,∀𝑡 .
1: Pretrain ℎ(·) and 𝑔(·) using historical observational data.
2: for 𝑡 = 1, 2, . . . do3: Receive new data 𝒙𝑖,𝑡 , 𝑌𝑜𝑏𝑠
𝑖,𝑡, 𝑌𝑛𝑜𝑟
𝑖,𝑡, 𝑑𝑜
𝑖,𝑡,∀𝑖 .
4: Update ℎ(·) and predict (𝑑𝑜𝑖,𝑡, 𝑌𝑜
𝑖,𝑡) using (3).
5: Update 𝜽𝑡 using (7).6: for 𝑖 = 1, . . . , 𝑁 do7: for 𝑘 = 1, 2, . . . ,𝑇𝑖,max − 𝑡 + 1 do8: Predict 𝑍𝑖 𝑗𝑘 and 𝑌𝑖 𝑗𝑘 (𝑑𝑖𝑘 ),∀𝑑𝑖𝑘 ∈ D𝑖 .
9: end for10: Optimize 𝑑∗
𝑖,1 using (16) and (17).
11: end for12: 𝑝∗
𝑖,𝑡= 𝑝𝑖,0𝑑
∗𝑖,1.
13: end for
number of the shops. It is easy to see that our algorithm is much
more efficient than the traditional dynamic programming algorithm
when |J | is large. In practice, our algorithm can be further pruned
by reducing redundant computation.
5.4 ExtensionThe counterfactual prediction and optimization framework is quite
general and can be applied into other scenarios of e-commerce
platform:
• In fresh retail scenario, this approach can also be applied for
the markdown of daily-fresh goods, which has only one day
shelf life. It aims to boost sales by cutting the price before
the end of the day, such as only two hours left.
• In the marketing scenario, it can be applied for personalized
coupon assignment task, which aims to maximize the overall
Return on Investment (ROI) of the platform by assigning the
different coupons to different users with budget constraint.
• In the customer service scenario, it can be applied for person-
alized compensation pay-outs task, which aims to maximize
the satisfaction rate of customers by offering the optimal
pay-outs for users with the budget constraint.
In above three examples, the treatment is price, coupon and com-
pensation pay-outs respectively, the outcome is the sales of product,
the conversion rate and satisfaction rate of the users respectively,
and the optimization objective is overall profit, ROI and satisfac-
tion rate respectively. To solve these problems, we first build the
causal relationship between treatment and outcome based on semi-
parametric model, and then optimize the objective with budget or
inventory constraints. It is worth noting that we have presented a
marketing budget allocation framework for the second scenario in
our previous work [37]. While, in this paper, the proposed coun-
terfactual prediction-based framework is more general and can be
applied into more scenarios.
6 EXPERIMENTTo evaluate the performance of the proposed approach, we apply
the markdown pricing algorithm in a real-world e-commerce fresh
retail - Freshippo. To reduce cost and stimulate consumption, Fre-
shippo will give a discount for the product whose sales performance
is not satisfactory. It will be sold in markdown channel, where cus-
tomers can buy goods by discount if their total purchase reached a
certain amount. Our aim is to help the retailer of Freshippo to decide
which optimal discount price of a product to be set to maximize
the overall profit.
6.1 Offline ExperimentTo optimize the price with business constraints, the first step and the
key step is to learn the price-demand curve as described in Section
4. We use the offline transaction data of Freshippo to train and
evaluate the proposed semi-parametric structural demand model.
We collect observational data in markdown channel over more than
100 fresh stores across 10 different cities in China over 6 months.
There are about 11000+ SKUs in total (we omit the exact number
for privacy-preserving). The detail of feature extraction is provided
in Supplement.
Learning model. Using the extracted features, we use XGBoost
[7] as our base sales forecasting model. The deep neural network
is also recommended when there are sufficient data samples for
training [3, 12]. Using the predicted base-discount and sales as in-
puts, we solve the objective (7) by recursive least squares algorithm,
and the price elasticity 𝜽 is updated in the recursion fashion. In
the Freshippo scenario, the price elasticity is daily updated once
the new transaction data is collected and features are automatically
extracted.
Evaluation metric. To evaluate the predictive ability of our semi-
parametric model, we predict the sales of the next day in markdown
channel with the actual discount of that day. The results are mea-
sured in Relative Mean Absolute Error (RMAE), defined as:
RMAE =
∑𝑁𝑖=1 |𝑌𝑖 − 𝑌𝑖 |∑𝑁
𝑖=1 𝑌𝑖, (19)
where 𝑁 is the number of the test samples, 𝑌𝑖 is the ground truth
sales and 𝑌𝑖 is the predicted sales.
Parameter settings. To tun the model hyperparameters, we split
data into training, validation and test data according to the time:
first 65% for training, next 15% for validation and last 20% for
testing. For price elasticity model, we empirically set the forgetting
factor 𝜏 = 0.95, the regularization parameter _ = 0.5.
Comparison algorithm. We compare the proposed model with
the classical boost tree model and deep model.
• XGBoost. This powerful boost tree model has been applied
in many industrial applications. For counterfactual predic-
tion task, we treat the discount variable as one of its input
features, and predict the outcome by varying discount with
other features fixed. For the sake of fairness, its hyperparam-
eters are set the same as our base sales forecasting model.
• DeepIV [13]. This method use deep model to characterize
the relationships between treatment and outcome in the
10 20 30 40 50 60 70 80 90 100Proportion of training data (%)
42.5
45.0
47.5
50.0
52.5
55.0
57.5
60.0
RMAE
(%)
TreeDeepIVSemi-parametric
Figure 6: The comparisons between tree model, deep model,and our semi-parametric model under different proportionof training data.
presence of instrument variables. We use the average price
of third-level category as the instrument variables, and use
Gaussian distribution for continuous treatment.
Results: Wefirst evaluate the prediction error of each algorithm
with different proportion of training data. As shown in Figure 6,
the deep model has poor performance with small training data.
The tree model is relatively insensitive with the data size but its
performance is poor even when there are more data available. Our
proposed semi-parametric model achieve the best RMAE perfor-
mance and its variance is reduced with the increase of the number
of training data. To further illustrate the interpretability of the pro-
posed model, we plot four price-sales curves of randomly chosen
SKUs in a random store in Figure 7. The curve learned by the tree
model has unpredictable jitter, and its outcome keeps unchanged
in a large range of discount (0.5-0.6, 0.8-1.0). The curve learned by
deepIV is almost a line, which indicates the sales is independent
with the price. Both tree and deep model can not correctly reveal
the price-sales relationship and the inferred results are not credible.
While, our semi-parametric model is much smoother and reveals a
monotonous relationship between price and sales. The variation
between close prices is small, which is consistent with the intuition.
6.2 Online A/B TestingWe evaluate our markdown approach in a online fresh retail, Fre-
shippo, as shown in Figure 1. Traditionally, the retailer of Freshippo
uses a manual pricing strategy that chooses an empirical discount,
such as 30% off or 50% off. Although the manual pricing strat-
egy is simple, it is the fruit of experience of operations for many
years and it works in most cases. The target products, which are
required for markdowns, are provided by the inventory control sys-
tem of Freshippo. The target sales and min-max price constraints
are given by fresh operational staff. Once got the signal of mark-
downs, the intelligence marketing system of Freshippo will call our
pricing algorithm to offer the optimal discount. Our algorithm has
been applied in the fresh stores in four regions, Beijing, Shanghai,
Hangzhou and Shenzhou.
Table 1: Target completion rate and GMV improvement
TCR𝑛𝑜𝑟 TCR𝑚𝑑 TCR𝑡𝑜𝑡𝑎𝑙 GMV_IMP
Operations 34.25% 46.68% 80.93% 101.49%
Ours 38.92% 53.20% 92.12% 118.63%
For fair comparison, we design the online A/B testing. The prod-
ucts required to be taken a discount are randomly assigned to the
operation’s manual approach and our markdown approach.
Evaluation metrics. To evaulate the performance of the proposed
algorithm, we use the target completion rate (TCR) as the metric,
defined as
TCR𝑛𝑜𝑟 =
∑𝑁𝑖=1 #SALES𝑖,𝑛𝑜𝑟∑𝑁
𝑗=1 𝐵𝑖,
TCR𝑚𝑑 =
∑𝑁𝑖=1 #SALES𝑖,𝑚𝑑∑𝑁
𝑗=1 𝐵𝑖,
(20)
where #SALES𝑖,𝑛𝑜𝑟 and #SALES𝑖,𝑚𝑑 denote the sales in the normal
channel and the sales inmarkdown channel, respectively. The target
completion rate assesses the effect on clearance of markdowns.
Besides, we also evaluate the ratio of Gross Merchandise Volume
(GMV) between normal channel and makdown channel, namely
GMV_IMP =
∑𝑁𝑖=1 𝑑𝑖𝑝𝑖#SALES𝑖,𝑚𝑑∑𝑁𝑖=1 𝑝𝑖#SALES𝑖,𝑛𝑜𝑟
. (21)
This metric evaluates the GMV improvement after markdowns.
Results . The A/B testing is carried out about 2 months. As
shown in Table1, the target completion rate of operation’s group is
about 34.25% before markdown, and this number goes to 80.93%after markdowns. While the target completion rate of our group is
about 38.92% before markdown, and this number goes to 92.12%after markdown. It indicates that our approach can better achieve
the clearance target than the maunal approach. Besides, the GMV
improvement of our pricing algorithm is higher about 17.14% than
that of maunal approach. This result shows that our approach can
help retailer obtain the higher GMV/profit.
In summary, our pricing algorithm is easy to explan as it has
interpretable price-sales curve, and it is intelligent as it can auto-
matically offer optimal price with high profit in consideration of
complex business constraints, such as inventory constraint.
7 CONCLUSIONIn this paper, we present a novel pricing framework for markdowns
in e-commerce fresh retails, consisting of counterfactual prediction
and multi-period price optimization. Firstly, we propose a data-
driven semi-parametric structural demand model, which has both
predictability and interpretability. The proposed demand model
reveals the relationship between price and sales and can be used
for predicting counterfactual demand with different prices. The
proposed counterfactual model has a lower model complexity and
a clear causal structure, therefore it is much more interpretable
than traditional ML and deep model. Secondly, we take the demand
uncertainty into consideration, and present a dynamic pricing strat-
egy of perishable products in a multi-period setting. An efficient
0.5 0.6 0.7 0.8 0.9 1.0discount
5
10
15
20
25
30
35
40
sale
s
SKU ASKU BSKU CSKU D
(a) Tree model
0.5 0.6 0.7 0.8 0.9 1.0discount
5
10
15
20
25
30
35
40
sale
s
SKU ASKU BSKU CSKU D
(b) DeepIV model
0.5 0.6 0.7 0.8 0.9 1.0discount
10
20
30
40
sale
s
SKU ASKU BSKU CSKU D
(c) Proposed semi-parametric model
Figure 7: Price-sales curves of four randomly chosen SKUs. The error bar denotes the mean and the standard deviation ofhistorical observed sales.
two-stage algorithm is proposed for solving the MDP problem. It
reduces the time complexity from exponential to polynomial. Fi-
nally, we apply our framework into a real-world e-commerce fresh
retail. Both offline experiment and online A/B testing show the
effectiveness of our approach.
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A SUPPLEMENTA.1 ImplementationIn order to improve the reproducibility, we present more details
about the implementation.
A.1.1 Software versions. The details of programming languages,
software packages and frameworks used in the experiments and
